Although, to be honest, there are no really valid data regarding the rate of change. No one can say whether a climate change 2 million years ago took place within 100 or 1,000 years. Measurements from ice cores, etc., do not really provide that, there are large uncertainties...
What is striking, however, is the correlation between the beginning of industrialization, that is the use of fossil fuels, and climate change. This is difficult to refute if one wants to argue seriously. Just the distance to the sun and sunspots... that will be difficult...
But... and this is where science begins. There is no 100% proof, that is, no empirical or model-based evidence. These are probabilities. And in the case of a probable catastrophe, one should of course always err on the safe side.
I seriously doubt that the transition from a warm period to the last ice age took millennia. That contradicts the climate theory of the "tipping point," which climate activists like to invoke.
One can only acknowledge one truth. Either there are tipping points that lead us extremely quickly into catastrophe. Or a change takes place slowly over millennia. Then, it really does not matter to us and future generations whether we do anything at all.
PS: And this is also important for people. I can still consider the generation of my grandchildren, although I will probably never see them. But the generation of the grandchildren's grandchildren? That is too far away to motivate me...
A lot is getting mixed up here.
For 2 million years ago, the temporal resolution from ice core data is good enough. Not for 50 million years ago.
The speed has nothing to do with whether there are tipping points and where they are. The periodic change between warm and cold periods is due to the Milankovitch cycles, which are changes in the Earth's orbit on ten-thousand-year rhythms. This modulates the solar constant, that is, the energy that arrives from the sun to the Earth.
For anthropogenic global warming and its cause, there are indeed very clear empirical proofs. Probably the second best empirically supported physical description after quantum mechanics. However, to project this into the future, where no one knows the exact emissions, computational models with assumptions and uncertainties are of course required, what else?
Tipping points also do not lead "immediately" to any catastrophes. If the Greenland ice sheet tips, its melting still takes about 8,000 years or so. One does not exclude the other. Whether that then is a catastrophe can only be judged afterwards.
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There are surprisingly many misconceptions on this topic — please do not take this personally, I am simply stating facts.